Answer :

Let the energy be proportional to m and c with powers p and q respectively

E mp cq

Dimensions of E = [ML2T-2]

Dimensions of m = [M]

Dimensions of c = [LT-1]

Let us assume a dimensionless constant K such that

E=Kmp cq


[ML2T-2] = [M]p[LT-1] q


On comparing, p=1 and q=2

So the relation between mass, speed and energy is


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